An example of \(\mathbb {M}\)  is the Gaussian mechanism.
When \(\mathcal {U} = \mathbb {R}^n\) , \(\mathcal {N}(0, \sigma ^2 I)\)  is added to the output \(\mathbb {M}(d)\) , and the norm on \(\mathcal {U}\)  is the \(\ell ^2-\) norm.
When \(\mathcal {U}\)  is a reproducing kernel Hilbert space (RKHS), the norm is the RKHS norm [1]}, and a Gaussian process noise \(\mathcal {G}(0, \sigma ^2K)\)  is added to \(\mathbb {M}(d)\) .
